Cyclo cross towards the recreational end of the spectrum. They'll take fast 700C road tires or wider tires for gravel. They still have drop bars where the hood position is more ergonomic than a flat bar and unlike bar-ends allows using the brakes and shifters without moving your hands. They're available at all price points.

"Unpaved" and "road bike" both cover a lot of ground. 23mm road tires ride fine on packed dirt roads that aren't washboarded, but won't work on anything soft. Some road bikes won't clear tires larger than that, some are set up with caliper brakes to clear tires 30mm wide that are be nice on gravel (I used 27mm cyclocross tires with my Litespeed on snow days in Colorado), and touring bikes have cantilever brakes that will clear wider tires if the frame can.